量子散度强数据处理不等式的张量化性质的反例
Counter-examples for Tensorization Property of Strong Data Processing Inequality for Quantum Divergences
浏览论文内容
中文总结 AI 辅助
该研究针对量子散度强数据处理不等式的张量化性质，通过构造反例证明量子卡方散度和量子相对熵的该性质均不成立，填补了相关一般性理解的空白。
中文摘要 AI 辅助
数据处理不等式是描述信息通过噪声信道时发生损失的基础性质，更精细的描述由强数据处理不等式（SDPI）刻画。在经典信息论中，强数据处理不等式的张量化性质对整个f-散度族成立，但其量子对应情况尚不清楚。此前仅在部分特殊情形下证明了量子SDPI的张量化性质，关于量子散度SDPI张量化性质的一般性理解仍未解决。本研究报告两个否定结果：量子卡方散度的张量化性质不成立，量子相对熵的张量化性质也不成立。
英文摘要
The data processing inequality is a fundamental property that describes the loss of information through noisy channels. A more refined description is characterized by the strong data processing inequality (SDPI). In classical information theory, the tensorization of strong data processing inequality holds for a whole family of $f$-divergences. However, its quantum counterpart is less known. The tensorization of SDPI was shown only for some special cases previously, and the general understanding about the tensorization property of SDPI for quantum divergences remains open. In this work, we report two negative results: the tensorization property fails for certain quantum chi-square divergences, and it also does not hold for the quantum relative entropy.
